Some Unified Properties And Its Teaching Study Of Conic Tangent

Conic curve is the core content of mathematics in college entrance examination.The problems related with conic tangent is also a difficulty.They often occur in college entrance examination. When solving this kind of problems, students often do not know how to start due to know too little property about these.Many students are tired of learning because of large and complicated calculation.By reading the classic book Apollonius of Perga Conics, the article organize and prove three basic uniform properties about the tangent of conics.These basic properties are mainly the relationship between tangents and other concepts such as vertical and diameter.From many unified properties,we select three groups of cross ratio properties,and point out the relationship between these properties.According to the actual situation of high school mathematics,We design a teaching case about the cross ratio property in diameter,and put forward that by induction and analogy in teaching, starting from the most basic round, guide students to extend the property of the round to other conic.This will be able to broaden the students' thinking,and can make the students feel the inner unified beauty of mathematics.By combining the conic equation given by Apollonius and oblique coordinate system theory,we put forward with the establishment of oblique coordinate system to prove properties of conic curve.The unified properties about the conic tangent put forward in this article can also be used as the basis of analytic geometry proposition,and has a certain reference value for the teachers and students as well as the proposition.